Elliptic curve isogeny class 3136.3-c over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-3136.3-c
• Conductor: 3136.3
• Rank: \( 0 \)

Base field \(\Q(\sqrt{2}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 2 \); class number \(1\).

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 3136.3-c over \(\Q(\sqrt{2}) \)

Isogeny class 3136.3-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
3136.3-c1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 20 a + 20\) , \( -92 a - 122\bigr] \)
3136.3-c2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 32 a - 48\) , \( -48 a + 66\bigr] \)
3136.3-c3	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -34 a + 46\) , \( -29 a + 45\bigr] \)
3136.3-c4	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 81 a - 125\) , \( 523 a - 747\bigr] \)